A Finite Difference Method of High Order Accuracy for the Solution of Two-Point Boundary Value Problems

Abstract

We present a new high order finite difference method for second order differential equation y''=f(x,y)  subject to boundary conditions y(a)=alpha and y(b)= beta. The method is based on rational function approximation and its development is based on power series expansions. Under appropriate conditions, local truncation error calculated and order of method estimated six. Our finite difference method leads to nonlinear system of equations. Numerical examples are given to illustrate the effectiveness, efficiency and high order accuracy of the method.